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United States competition problems

Number theory Difficulty 4.2 AIME Find the answer United States

Problem:

What is the remainder when $100!$ is divided by $101$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

Wilson's theorem says that for $p$ a prime, $(p-1)! \equiv -1 \pmod{p}$ , so the remainder is $100$ .

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